Question

If cos²alpha = sin alpha.tan alpha, find cot³ alpha - cot⁶ alpha​

Answer 1

Answer:

${cos}^{2}α \: = \: sinα \times tanα \\ {cos}^{3}α \: = \: {sin}^{2} α \\ {cos}^{6}α= {sin}^{4} α \\ to\: find,\:{cot}^{6} α− {cot}^{2} α \\ ⇒ \frac{ {cos}^{6} α}{ {sin}^{6} α} − {cot}^{2} α \\⇒ \frac{1}{ {sin}^{2} α} − \frac{ {cos}^{2}α }{ {sin}^{2}α } = \frac{1 - {cos}^{2} α}{ {sin}^{2} α} = \frac{ {sin}^{2}α }{ {sin}^{2}α } =1$